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Simplifying 2y2 + -10y = 5 Reorder the terms: -10y + 2y2 = 5 Solving -10y + 2y2 = 5 Solving for variable 'y'. Reorder the terms: -5 + -10y + 2y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5y + y2 = 0 + 2.5 -5y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5y + y2 = 2.5 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 2.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5y + y2 = 8.75 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (y + -2.5) equal to 2.958039892 and -2.958039892.Subproblem 1
y + -2.5 = 2.958039892 Simplifying y + -2.5 = 2.958039892 Reorder the terms: -2.5 + y = 2.958039892 Solving -2.5 + y = 2.958039892 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.958039892 + 2.5 y = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 y = 5.458039892 Simplifying y = 5.458039892Subproblem 2
y + -2.5 = -2.958039892 Simplifying y + -2.5 = -2.958039892 Reorder the terms: -2.5 + y = -2.958039892 Solving -2.5 + y = -2.958039892 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.958039892 + 2.5 y = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 y = -0.458039892 Simplifying y = -0.458039892Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.458039892, -0.458039892}
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